The mechanical properties of the material directly affects the safety and life of the components, and the elastic constants of materials is an important index of its mechanical properties. The finite element software Abaqus is used to simulate the propagation of Rayleigh surface wave and longitudinal wave laser excitation in the dissemination process of sheet metal sample surface and in vivo. Effect of pulse laser on the sample used is equivalent to the modified Gauss distribution power source to generate the ultrasonic. The infinite element at the boundary is set to eliminate the interference signal echo, and receive the ultrasonic signals to calculate the velocity of Rayleigh surface wave and longitudinal wave. According to the relationship between velocity and elastic constants, elastic constants is detected. The numerical results are in good agreement with theoretical solution, thus a very effective numerical method for laser ultrasonic detection of elastic constants of materials to provide.